Magnetic Resonance Imaging (MRI) or Nuclear Magnetic Resonance (NMR) imaging generally provides spatial discrimination of resonant interactions between radio frequency (RF) waves and atomic nuclei in a magnetic field. Specifically, MRI utilizes hydrogen nuclear spins of the water molecules in the human body, which are polarized by a strong, uniform, static magnetic field, commonly referred to as B0 or the main magnetic field. When a substance, such as human tissue, is subjected to the main magnetic field, the individual magnetic moments of the spins in the tissue attempt to align with the main magnetic field. When excited by an RF wave, the spins precess about the main magnetic field at a characteristic Larmor frequency. Signals are emitted by the excited spins, which are processed to generate Magnetic Resonance (MR) images of the subject.
The electrical properties of substances, such as human tissue, determine their interaction with the radio-frequency fields used in MRI, are useful to know for certain reasons, and could be measured from MRI exams. For example, determination of the electrical properties of tissue (conductivity and permittivity) are useful in estimating local RF power deposition (also known as local specific absorption rate or abbreviated as SAR) during acquisition of MR images. The electrical properties of tissue can also be useful in discriminating between malignant and healthy tissue (e.g., malignant tissue has been shown to have higher permittivity and conductivity than surrounding healthy tissue). In some applications, knowledge of the electrical properties of tissue can be used during therapeutic applications of heat using radio frequency, e.g., RF hyperthermia for treatment planning.
Determining the electrical properties of tissue in-vivo using MRI has posed several problems due to the inability to directly measure the complex values (magnitude and phase) of the receive RF magnetic field B1− and the transmit RF magnetic field B1+. To overcome this limitation, conventional approaches using MRI have estimated the electrical properties of tissue using the transmit RF magnetic field B1+ for example, by mapping the amplitude of the transmit RF magnetic field and approximating the phase of the transmit magnetic field. Conventional MR-based electrical property measurement techniques typically rely on mapping the transmit RF field B1+, by attempting to eliminate the effect of the receive RF field B1− from the MR images used for the measurements. The amplitude of B1+ can be obtained using various approaches, such as Bloch-Siegert B1+ mapping and/or the double-angle method. The phase of B1+, on the other hand, is generally more difficult to separate from the phase of the measured signal. Methods have been proposed to approximate the phase of B1+. Using conventional methods, a complex map of B1+ is formed and the map is subjected to Laplacian operation to produce k2 (complex wave vector) maps and subsequently electrical properties maps.
While conventional approaches have provided techniques for estimating the electrical properties of tissue based on mapping the amplitude of B1+ and approximating the phase of B1+, implementations of the conventional B1+ mapping approaches may require specialized MRI sequences, not existing on all clinical scanners. Even if they exist on a scanner, these sequences tend to be signal to noise ratio (SNR) inefficient for the purpose of estimating electrical properties, requiring a rather lengthy acquisition time.